So, what is an Xray signature from a star? Is it a heat sugnature, or an electon bombardment signature?

In a Xrays are produced in regions of gas (plasma, actually) where the temperature reaches upwards of a million or so degrees kelvin. In our sun, for example, like chance says, the Proton-Proton reaction in stars creates gamma rays (not xrays) 4 per reaction. However, it takes a energy created by one photon photon reaction uptwards of a million years to reach the surface of the star, and by that time it's not 4 gamma ray photons, but many many more visible light photons of all sorts of wavelengths that we see with our eyes, and feel on our skin each day. If you want, there is a great demo that is available online here that really talks about this in detail.

However, the environment around the sun does produce X-rays in its own right, and the first time anyone pointed an Xray detector, they we very surprised to see Xrays around the sun. Like you say, they shouldn't be there and no one is quite sure why the observed temperature is 6000 degrees at the surface of the sun, but is a few million degrees kelvin right above the solar surface, in a region called the corona. Outside of stars, Xrays can be created by events called shocks, where a wave of energy (say from a nearby exploding supernova) passing through a dust cloud compresses the gas in a way that makes it emit Xrays.

To answer your question: Xrays seen in astrophysics are usually caused recombination of electrons and atoms, like Iron, or by Compton Scattering. Some are caused by synchrotron radiation. Each case leaves a very specific spectral indication which allows you to determine what you are seeing, in the case of recombination, it is a heat signaure, but in the other cases, it doesn't have much to do with heat, but is an indicatore of things like the magnetic field of the object, or other indicators.

I think the general misconception here is that because the moon is going further away quite quickly, then other binary systems must do it also. And the faster they orbit the quicker this happens.

What is an orbit?

Basically an object in orbit is seemingly perpetually falling towards an object. 'Freefall' as the call it. Imagine firing a cannon off, what happens? The ball moves in two directions. One is horizontal, making it travel away from the cannon. The other is vertical, making it travel towards the ground. The two motions combine so the path looks a like a curve. Imagine getting a bigger cannon that fired the ball faster. The curve would be more gentle, the ball would go further. Imagine now, getting a cannon so big that it fires the ball so hard that this curve is so gentle that it matches the curve of the earth. It would be constantly falling towards the earth but it would never get there (if we conveniently ignore friction and hazards for a moment).

So why does the Moon seem to be getting further away from the Earth?

When the moon orbits us, its gravitational influence, causes the Earth to be attracted to it. This has a tidal effect on the earth. The tidal effect attempts to slow the moon down. Slowing the moon down is hard work. This work transfers energy from the Earth to the Moon, causing the moon's orbit to increase.

Binary starsImagine a binary system composed of two identical objects. There would be no energy transfer like from the Earth to Moon, or rather if there were such a transfer it would be equal, so the net energy transfer is 0. Thus, the orbits don't increase.

As for the question: how do stars form, clouds don't collapse in on themselves!

Gravity and mass go hand in hand. If we have a huge cloud of gas the mass of Jupiter, that cloud of gas has gravity. Each gas molecule exerts a little bit of gravitational influence building up to one big one. The mass of Jupiter (Which is woefully small compared to our sun), is 1.8987 Ãƒâ€” 10^27 kilograms. Thats a lot of gravity.

Imagine being a mole of hydrogen (mass = 2gram) near (about 1600 metres (a mile) away) from this massive cloud. In order to not be 'sucked in' it would need the following amount of force:

984,867,187.5 Newtons. Its unlikely that our nearby mole of hydrogen will have that amount of Force applied to it, so it gets sucked in. All the moles of gas in the nearby area have the same problem and eventually they form into a sphere. We call these spheres, gas giants. The gravity is keeping the gas together. Imagine, if the mass of our gas giant was so great, that the gravity was so immense, that nuclear fusion took place in it. We now, amazingly, have a star. Is it possible that this happens today? There is no law, or reason to think otherwise.